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# Numerical Integration and Differentiation

## Functions

## Topics

Quadratures, double and triple integrals, and multidimensional
derivatives

`integral` |
Numerical integration |

`integral2` |
Numerically evaluate double integral |

`integral3` |
Numerically evaluate triple integral |

`quadgk` |
Numerically evaluate integral, adaptive Gauss-Kronrod quadrature |

`quad2d` |
Numerically evaluate double integral, tiled method |

`cumtrapz` |
Cumulative trapezoidal numerical integration |

`trapz` |
Trapezoidal numerical integration |

`polyint` |
Polynomial integration |

**Integration to Find Arc Length**

This example shows how to parametrize a curve and
compute the arc length using `integral`

.

This example shows how to calculate complex line integrals using the `'Waypoints'`

option of the `integral`

function.

**Singularity on Interior of Integration Domain**

This example shows how to split the integration domain to place a singularity on the boundary.

**Analytic Solution to Integral of Polynomial**

This example shows how to use the `polyint`

function to integrate polynomial expressions analytically.

This example shows how to integrate a set of discrete velocity data numerically using `trapz`

to approximate the total distance traveled.

**Calculate Tangent Plane to Surface**

This example shows how to approximate gradients of a function by finite differences.

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